some thoughts on fission yield data in estimating reactor ...some thoughts on fission yield data in...

Some thoughts on Fission Yield Data in Estimating Reactor Core Radionuclide Activities (for anti-neutrino estimation)

Dr Robert W. Mills,NNL Research Fellow for Nuclear Data,UK National Nuclear Laboratory.

R.W. MillsWorkshop on Reactor Neutrinos

6-8 November 20132

Summary

• Introduction

• Fission Yield Evaluation• Evaluation

• Measurements and their analysis

• Models

• Adjustment

• Cumulative and independent yield uncertainty estimation

• Error propagation in nuclear codes• “Total Monte Carlo”

• Probability distribution functions

• Summation example using TENDL decay heat

• Some FISPIN calculations of anti-neutrinos in a Pressurised Water Reactor


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Introduction

• Anti-Neutrino production in reactors is a decay process and thus is dependent upon the summation over all radio-nuclides of the decay rate present multiplied by the probability of (anti-) neutrino production.

• This probability is equal to the + (or -) probability.

• This requires the number densities or activities of the radio-nuclides present in the core


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Introduction

• The production and destruction of all nuclides are governed by the standard equations:

• Depends on flux, cross-sections, fission yields, decay constants and branching ratios decay paths.


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Fission Yield Evaluation

What is nuclear data “evaluation”

• Can be described as the processing of giving numeric value to a quantity

…. but

• Has to be consistent with measurements and constraints of physical laws, at least within currently accepted knowledge.

• Has to be consistent with semi-empirical or theoretical models.

• Has to be reported/distributed in a form that all can use easily (e.g. ENDF format)


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History of UK evaluations

1960-1981 Crouch

Atomic and Nuclear Data Tables (1977)

1981-1987

James and Banai UKFY1 / JEF1 (1986)

1988-1995

Mills, James and Weaver UKFY2 / JEF-2.2 (1993)

1995-present

Mills UKFY3.x series - JEFF-3.1.1 (UKFY3.6A)

(UKFY4 photon, neutron and charged particle induced

energy dependent or spontaneous fission using Wahl code).


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Definitions


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Independent yields

• Direct probability of forming a nuclide after prompt neutron emission but before decay

• Needed for general inventory calculations

• Difficult to measure, especially for short half-lives or where corrections for major contributions from other nuclides’ decay need to be considered.

• In JEFF fits to Wahl Zp model are used to fill extrapolate from small number of measurements to complete set and then adjusted for physical constraints.

• Large uncertainties on values.


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Definitions


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Cumulative yields

• Probability of forming a nuclide directly after prompt neutron emission or by decay, or after a “long” irradiation at 1 fission per second = decay rate (production=destruction)

• Not used in inventory calculations

• Easier to measure and many more measurements

• In JEFF independent yields and decay data used to calculate and then merged with experimental data and their uncertainties using an adjustment process and a “backward-forward” error calculation.

• Smaller uncertainties on values with expt. data


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Data Analysis• UKFY3 based upon experimental data from >2000 papers, reports etc. • Measurements analyzed to given “best estimates”

of each measured yield


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Mass distribution


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Mass distribution


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Charge distribution (Wahl Zp)


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Isomeric splitting of yields


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Ternary fission(light charge particle emission)


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Adjustment to physicalconstraints


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Validation


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• Given the individual decay branches for all nuclides in the decay paths from one nuclide to a distant daughter it is possible to calculate the fraction of j that decays to i

• If Qi,i is defined as 1 and Qk,i =0 (where k does not decay to i), Thus any cumulative yield can be calculated from the independent yield.

Fission Product Yields-Q matrix method


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Uncertainty propagation

• As this is a Q weighted sum of Yi then the variance of the result is given by

• If all terms expect the covariance is known, these can be calculated.


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“Forward-Backward” technique

• C is weighted sum of independent yields

C(Z) = I(Z) + I(Z-1)*Q(z-1,z) + I(z-2)*Q(z-2,z) + …

C(Z+1)= I(Z+1) + Q(z,z+1) * ( I(Z)+ I(Z-1)*Q(z-1,z) + I(z-2)*Q(z-2,z) + …)

C(Z+1)= I(Z+1) + C(Z) * Q(z,z+1)


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“Forward-Backward” technique

C(Z) = (C(Z+1) – I(Z+1) ) / Q(z,z+1)

• Equation is now a function of only one cumulative yield, one independent yield and decay data.

• If you know C(Z+1) and its error from measurement and have an estimate of its independent yield and uncertainty can determine uncertainty of C(Z).

• In JEFF-3.1.1, if C(Z) has been adjusted by x to fit independent yield constraints then uncertainty is increased by x.


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Mass 85 example

• What does the Q matrix look like


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Effect on cumulative yield uncertainties

• The following shows the JEFF-3.1.1 file data and a calculation of Yc and its uncertainty without the covariance terms.

• The results show that without the covariance terms the yields are over-predicted.


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“Total Monte Carlo”

• Monte Carlo method is a well understood technique where random sampling of variables is used to solve a mathematical or physical problem.

• “Total Monte Carlo” is where you randomly adjust the parameters going into the evaluation to produce randomised data sets each of which can then be run through a problem to give an output probability distribution on a parameter based upon the entire set of randomised nuclear data that because the evaluation ensure consistency will agree with physical constrains.

- e.g. TENDL


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Simple “Total Monte Carlo” for practical decay data example

• Consider a mass of plutonium containing an initial activity of 241Pu and 241Am. How do these vary with time and what are their uncertainties?

• Given the decay constants are 4.8134x10-2 ± 3.342x10-4 per year and 1.6019x10-3 ± 1.852x10-6 per year respectively.

• The “best estimate” result can easily be calculated.

• If we sample the decay constants from different probability distributions with the required mean and standard deviation, run each for 10000 times and then analyse the results we get ….


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Probability Distribution functions

0

50

100

150

200

250

300

350

400

0.046 0.047 0.048 0.049 0.05

Linear

Normal

LogNormal


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Result

At 200 years

PDF 241Pu 241Am

Normal 10.13±

0.68

3933±

28

Linear 10.12±

0.67

3933±

28

LogNormal

10.13±

0.68

3933±

27

Activities at200 years


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Plot of 255 241Pu decay curvesfrom normal distribution calcs

1

10

100

1000

10000

100000

1000000

0 50 100 150 200


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Larger uncertainties

• In nuclear data work it is often necessary to consider larger uncertainties, even orders of magnitude.

• Repeating the calculations using 50 percent uncertainties on the decay constants, we get activities at 200 years for

241Pu activities of

4.62x105±3.42x107,

560±1762

and

2595±7094

(should be 10.1)

and 241Am activities of

18946±727627,

4683±2888

and

5522±5221

(should be 3933)


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Larger uncertainties

• Why?

• Mean and standard deviations of 241Pu λ are

• Normal 0.048224 ± 0.02405

• Linear 0.048175 ± 0.02411

• LogNormal 0.048210 ± 0.02403

• Compared to input 0.048134 looks okay!

• Examining PDFs and results …


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Probability Distribution functions

0

100

200

300

400

500

600

-0.1 0 0.1 0.2 0.3

Linear

Normal

LogNormal


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Plot of 255 241Pu decay curvesfrom normal distribution calcs

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

1000000

10000000

0 50 100 150 200


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Decay exampleConclusions

• This shows the method fails with high uncertainties, resulting from their physical interpretation.

• What do these large uncertainties mean?

• An uncertainty of, say, > 35 percent has little meaning without specifying its distribution and any constraints on the value from the expt. analysis, theoretical model or evaluation process.

• For example λ must be greater than zero.

• Without these it may only be possible to quote a "best estimate" result.


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Fission Product decay heat following a fission pulse

• TENDL-2010 included FPY and decay data files with up to 1000 randomly perturbed data libraries for used in uncertainty propagation.

• Using these FPY libraries, the UK spent fuel inventory code FISPIN was used to calculate decay heat from a fission pulse with each library.

• The unperturbed JEFF-3.1.1 decay data library was used and thus the uncertainties from energy release per decay and half-lives are not considered. Although some published Algora/Tain TAGS data was included extending JEFF-3.1.1.

• The results were compared Tobias (1989).


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239Pu total energy release

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5

Cooling time (s)

En

erg

y r

ele

ase

ra

te p

er

fis

sio

n x

tim

e

(MeV

/s / f

iss

ion

. s

)

Tobias (1989)

JEFF311+

TENDL

TENDL min

TENDL max


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235U total energy release

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5

Cooling time (s)

En

erg

y r

ele

ase r

ate

per

fissio

n x

tim

e

(M

eV

/s / f

issio

n).

s

Tobias (1989)

JEFF311+

TENDL

TENDL min

TENDL max


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239Pu -ray energy release

0.1

0.2

0.3

0.4

0.5

0.6

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5

Cooling time (s)

En

erg

y r

ele

ase

ra

te p

er

fis

sio

n x

tim

e

(MeV

/s / f

iss

ion

. s

)

Tobias (1989)

JEFF311+

TENDL

TENDL min

TENDL max


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235U -ray energy release

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1E+0 1E+1 1E+2 1E+3 1E+4

Cooling time (s)

En

erg

y r

ele

ase r

ate

per

fissio

n x

tim

e

(MeV

/s / f

issio

n).

s

Tobias (1989)

JEFF311+

TENDL

TENDL-min

TENDL-max


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239Pu -particle energy release

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5

Cooling time (s)

En

erg

y r

ele

ase r

ate

per

fissio

n x

tim

e

(MeV

/s / f

issio

n . s

)

Tobias (1989)

JEFF311+

TENDL

TENDL min

TENDL max


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235U -particle energy release

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5

Cooling time (s)

En

erg

y r

ele

ase r

ate

per

fissio

n x

tim

e

(MeV

/s / f

issio

n).

s

Tobias (1989)

JEFF311+

TENDL

TENDL min

TENDL max


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Fission Product decay heat following a fission pulse

• As expected the TENDL results show larger uncertainties at shorter times when more short-lived fission products contribute. Note scaling by multiplying by time, reduces value and uncertainties below 1 second.

• The results show the expected under-prediction for 235U gamma-ray energy release reported by other workers. As the corresponding beta particle energy release appears centred about the Tobias data it appears that this is more about fission yields rather than only a decay data effect.


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Anti-neutrino calculation

• Consider a typical modern PWR reactor containing 75.14 metric tonnes of uranium in a UO2 fuel with a 4.5% enrichment.

• Consider a mean rating of 45.833 MW/t (i.e. a total power of 3444 MW thermal) with fuel residing in the core for four 300 day cycles with 30 day gaps for refuelling and maintenance what neutrino source term would we expect.

• In a real core there will be variation both axially and radially in the core e.g. at the end of the assemblies where the power could considerably less.

• The following considers the mean power and to show effects 20% of this but with the same residency time.


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• Using the FISGUI (FISPIN Graphical User Interface) calculations of were made every 30 days during irradiation and shutdown, after the irradiation the fuel was considered as removed and cooled to 1, 30, 50, 100 and 365.25 days.

• The activities were then multiplied by the probability of - emission and summed to get the neutrino emission (i.e. no weighting by detection probability).


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Anti-neutrino emission rate (per second) per tonne of fuel against time in days.


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Fractional anti-neutrino contribution 30 days into cycle


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Fractional anti-neutrino contribution after irradiation


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• Anti-neutrino emission is approximately proportional to reactor power.

• Varies between 1.96E20 and 2.18E20 neutrinos per GW for a single assembly

• Small variation of value during irradiation ~10%.

• Assuming all fuel reaches the same final irradiation in 4 cycles an equilibrium core will have a starting value of 20.65 GWd/t and finishing value of 34.75 GWd/t (mid-point 27.5 GWd/t)

• Then expect neutrino emission to be nearer to 2.07E20 per GW with ~3% variation during cycle.

• In a real core expect variation to be larger.

some thoughts on fission yield data in estimating reactor ...some thoughts on fission yield data in...

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